scholarly journals THE NETWORK OF INTER-REGIONAL DIRECT INVESTMENT STOCKS ACROSS EUROPE

2007 ◽  
Vol 10 (01) ◽  
pp. 29-51 ◽  
Author(s):  
STEFANO BATTISTON ◽  
JOAO F. RODRIGUES ◽  
HAMZA ZEYTINOGLU
Keyword(s):  
Power Law ◽  
Direct Investment ◽  
Policy Making ◽  
Scaling Laws ◽  
Statistical Distributions ◽  
Regional Investment ◽  
Log Normal ◽  
Geographical Space ◽  
Log Normal Distribution ◽  
Different Levels

We present an analysis of inter-regional investment stocks within Europe from a complex networks perspective. We consider two different levels: first, we compute the inward–outward investment stocks at the level of firms, based on ownership shares and number of employees; then we estimate the inward–outward investment stock at the level of regions in Europe, by aggregating the ownership network of firms, based on their headquarter location. To our knowledge, there is no similar approach in the literature so far, and we believe that it may lead to important applications for policy making. In the present paper, we focus on the statistical distributions and the scaling laws, while in further studies we will analyze the structure of the network and its relation to geographical space. We find that while outward investment and activity of firms are power law distributed with a similar exponent, for regions these quantities are better described by a log-normal distribution. At both levels we also find scaling laws relating investment to activity and connectivity. In particular, we find that investment stock scales as a power law of the connectivity, as previously found for stock market data.

scholarly journals Extreme geomagnetic activities: a statistical study

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Ryuho Kataoka
Keyword(s):  
Magnetic Storms ◽  
Magnetic Observatory ◽  
Statistical Distributions ◽  
Limited Data ◽  
Data Set ◽  
Sudden Commencements ◽  
The One ◽  
Log Normal ◽  
Geomagnetic Activities ◽  
Log Normal Distribution

Abstract Statistical distributions are investigated for magnetic storms, sudden commencements (SCs), and substorms to identify the possible amplitude of the one in 100-year and 1000-year events from a limited data set of less than 100 years. The lists of magnetic storms and SCs are provided from Kakioka Magnetic Observatory, while the lists of substorms are obtained from SuperMAG. It is found that majorities of events essentially follow the log-normal distribution, as expected from the random output from a complex system. However, it is uncertain that large-amplitude events follow the same log-normal distributions, and rather follow the power-law distributions. Based on the statistical distributions, the probable amplitudes of the 100-year (1000-year) events can be estimated for magnetic storms, SCs, and substorms as approximately 750 nT (1100 nT), 230 nT (450 nT), and 5000 nT (6200 nT), respectively. The possible origin to cause the statistical distributions is also discussed, consulting the other space weather phenomena such as solar flares, coronal mass ejections, and solar energetic particles.

scholarly journals Comparative Study of Statistical Distributions in Electromigration-Induced Failures of Al/Cu Thin-Film Interconnects

1994 ◽  
Vol 16 (2) ◽  
pp. 119-126 ◽  
Author(s):  
M. I. Loupis ◽  
J. N. Avaritsiotis ◽  
G. D. Tziallas
Keyword(s):  
Thin Film ◽  
Grain Size ◽  
Extreme Value Distribution ◽  
Statistical Distributions ◽  
Post Processing ◽  
Failure Times ◽  
Life Data ◽  
Cu Thin Film ◽  
Log Normal ◽  
Log Normal Distribution

In electromigration failure studies, it is in general assumed that electromigration-induced failures may be adequately modelled by a log-normal distribution. Further to this, it has been argued that a lognormal distribution of failure times is indicative of electromigration mechanisms. We have combined post processing of existing life-data from Al/Cu + TiW bilayer interconnects with our own results from Al/Cu interconnects to show that the Log Extreme Value distribution is an equally good statistical model for electromigration failures, even in cases where grain size exceeds the linewidth. The significance of such a modelling is particularly apparent in electromigration failure rate prediction.

scholarly journals The Statistical Distributions of PM2.5 in Rayong and Chonburi Provinces, Thailand

2020 ◽  
Vol 8 (3) ◽  
Author(s):  
Vanida Pongsakchat ◽  
Pattaraporn Kidpholjaroen
Keyword(s):  
Fine Particulate Matter ◽  
Statistical Distribution ◽  
Distribution Model ◽  
Statistical Distributions ◽  
Average Data ◽  
Fine Particulate ◽  
Pearson Type ◽  
Anderson Darling ◽  
Log Normal ◽  
Log Normal Distribution

The fine particulate matter (PM2.5) concentrations is one of the most important issues that are often discussed since it has a greater impact on human health. Statistical distribution modeling plays an important role in predicting PM2.5 concentrations. This research aims to find the optimum statistical distribution model of PM2.5 in Rayong Province and Chonburi Province. The daily average data from 2014 – 2019 for Rayong and from 2015 – 2019 for Chonburi were using. Five statistical distributions were compared. A proper statistical distribution that represents PM2.5 concentrations has been chosen based on three criteria include Anderson-Darling statistic and RMSE. The results show that Pearson type VI distribution performs better compared to other distributions for PM2.5 concentrations in Rayong. For Chonburi, the proper statistical distribution is Log normal distribution.  

FROM LOGNORMAL DISTRIBUTION TO POWER LAW: A NEW CLASSIFICATION OF THE SIZE DISTRIBUTIONS

2006 ◽  
Vol 17 (10) ◽  
pp. 1429-1436 ◽  
Author(s):  
LUCIEN BENGUIGUI ◽  
EFRAT BLUMENFELD-LIEBERTHAL
Keyword(s):  
Normal Distribution ◽  
Power Law ◽  
Lognormal Distribution ◽  
Size Distributions ◽  
New Classification ◽  
Multiplicative Process ◽  
Random Multiplicative Process ◽  
Log Normal ◽  
Log Normal Distribution

We propose a new classification of the size distributions of entities based on an exponent α defined from the shape of the log–log Rank Size plot. From an inspection of a large number of cases in different fields, one finds three possibilities: α = 1 giving a power law, α > 1 (parabola like curve) and 0 < α < 1 (analogous to a log normal distribution). A fourth possibility that can be defined when α < 0 was never observed. We present a modified version of models based on a random multiplicative process and an introduction of new entities during the growth. We recover all three kinds of distributions and show that the type of a distribution is conditioned by the rate of the introduction of new entities.

scholarly journals Quasi-Static Variation of Power-Law and Log-Normal Distributions of Urban Population

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 908
Author(s):  
Atushi Ishikawa ◽  
Shouji Fujimoto ◽  
Arturo Ramos ◽  
Takayuki Mizuno
Keyword(s):  
Normal Distribution ◽  
Power Law ◽  
Time Variation ◽  
Time Reversal ◽  
Urban Population ◽  
Large Scale ◽  
Time Reversal Symmetry ◽  
Scale Range ◽  
Log Normal ◽  
Log Normal Distribution

We analytically derived and confirmed by empirical data the following three relations from the quasi-time-reversal symmetry, Gibrat’s law, and the non-Gibrat’s property observed in the urban population data of France. The first is the relation between the time variation of the power law and the quasi-time-reversal symmetry in the large-scale range of a system that changes quasi-statically. The second is the relation between the time variation of the log-normal distribution and the quasi-time-reversal symmetry in the mid-scale range. The third is the relation among the parameters of log-normal distribution, non-Gibrat’s property, and quasi-time-reversal symmetry.

scholarly journals Five decades of US, UK, German and Dutch music charts show that cultural processes are accelerating

2019 ◽  
Vol 6 (8) ◽  
pp. 190944 ◽  
Author(s):  
Lukas Schneider ◽  
Claudius Gros
Keyword(s):  
Power Law ◽  
Theoretical Approach ◽  
Opinion Dynamics ◽  
Profound Change ◽  
Personal Time ◽  
The Past ◽  
Time Horizons ◽  
Cultural Processes ◽  
Log Normal ◽  
Log Normal Distribution

Analysing the timeline of US, UK, German and Dutch music charts, we find that the evolution of album lifetimes and of the size of weekly rank changes provide evidence for an acceleration of cultural processes. For most of the past five decades, number one albums needed more than a month to climb to the top, nowadays an album is in contrast top ranked either from the start, or not at all. Over the last three decades, the number of top-listed albums increased as a consequence from roughly a dozen per year, to about 40. The distribution of album lifetimes evolved during the last decades from a log-normal distribution to a power law, a profound change. Presenting an information–theoretical approach to human activities, we suggest that the fading relevance of personal time horizons may be causing this phenomenon. Furthermore, we find that sales and airplay- based charts differ statistically and that the inclusion of streaming affects chart diversity adversely. We point out in addition that opinion dynamics may accelerate not only in cultural domains, as found here, but also in other settings, in particular in politics, where it could have far reaching consequences.

scholarly journals Is Mean Time to Failure (MTTF) Equal to Mean Time of Life for Unrepairable Systems?

2021 ◽  
Vol 51 (1) ◽  
pp. 255-264
Author(s):  
Leszek Opyrchał
Keyword(s):  
Wigner Distribution ◽  
Time To Failure ◽  
Statistical Distributions ◽  
Chi Square ◽  
Mean Time To Failure ◽  
Reliability Parameters ◽  
The Mean ◽  
Log Normal ◽  
Mean Time ◽  
Log Normal Distribution

Abstract One of the most important reliability parameters is the mean time to failure (MTTF). It is widely accepted that the MTTF is equal to the mean time of life ET. This article shows that this is not necessarily true. Although for the most commonly used statistical distributions (such as exponential, Gaussian, chi-square, Fisher-Tippett distributions) the values of MTTF and ET are equal, this is not the case for the log-normal distribution. Similarity, some less commonly used distributions (such as Breit-Wigner distribution) may also require calculation adjustments resulting from MTTF ≠ ET. Ignoring this discrepancy, an erroneous MTTF value can be obtained.

scholarly journals Extreme geomagnetic activities: A statistical study

2020 ◽  
Author(s):  
Ryuho Kataoka
Keyword(s):  
Magnetic Storms ◽  
Statistical Distributions ◽  
Limited Data ◽  
Data Set ◽  
Sudden Commencements ◽  
The One ◽  
Log Normal ◽  
Geomagnetic Activities ◽  
Log Normal Distribution ◽  
Power Law Distributions

Abstract Statistical distributions are investigated for magnetic storms, sudden commencements (SCs), and substorms to identify the possible amplitude of the one in 100-year and 1000-year events from a limited data set of less than 100 years. It is found that majorities of events essentially follow the log-normal distribution, as expected from the random output from a complex system. However, it is uncertain that rare events follow the same log-normal distributions, and rather follow the power-law distributions. Based on the statistical distributions, the probable amplitudes of the 100-year (1000-year) events can be estimated for magnetic storms, SCs, and substorms as approximately 750 nT (1100 nT), 230 nT (450 nT), and 5000 nT (6200 nT), respectively. The possible origin to cause the statistical distributions are also discussed, consulting the other space weather phenomena such as solar flares, coronal mass ejections, and solar energetic particles.

Fractal properties in fetal breathing dynamics

1992 ◽  
Vol 263 (1) ◽  
pp. R141-R147 ◽  
Author(s):  
H. H. Szeto ◽  
P. Y. Cheng ◽  
J. A. Decena ◽  
Y. Cheng ◽  
D. L. Wu ◽  
...  
Keyword(s):  
Time Series ◽  
Power Law ◽  
Power Spectra ◽  
Breathing Rate ◽  
Power Law Distribution ◽  
Inverse Power Law ◽  
Beta Power ◽  
Fetal Breathing ◽  
Log Normal ◽  
Log Normal Distribution

The dynamic pattern of fetal breathing was studied in 17 fetal lambs with chronically implanted electromyographic electrodes in the diaphragm. The instantaneous breathing rate time series appeared similar on different time scales, with clusters of faster breathing rates interspersed with periods of relative quiescience, suggesting self-similarity. Distribution histograms of the interbreath intervals (IBIs) showed log-normal distribution for IBIs less than 1 s and inverse power-law distribution for IBIs greater than 1 s. The ratio of log-normal distribution to power-law distribution varied from approximately 2 at 102 days to approximately 30 by 130 days of gestation. Fast Fourier transform of the breathing rate time series revealed 1/f beta power spectra for all animals, with beta increasing linearly from 0.43 to 0.88 between 102 and 139 days. Studies in the newborn lamb showed further maturation in both the distribution characteristics of the IBIs, as well as in the 1/f power spectra, with beta approaching 1.0 at 2 days after birth. The inverse power-law relationship in the distribution of the IBIs, together with the 1/f beta power spectra, indicate scale invariance and suggest that fractal mechanisms are involved in the regulation of fetal breathing.

scholarly journals The Probability Distribution of Worldwide Forest Areas

2021 ◽  
Vol 13 (3) ◽  
pp. 1361
Author(s):  
Rafael González-Val
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Power Law ◽  
Power Laws ◽  
Theoretical Models ◽  
Forest Growth ◽  
Plausible Model ◽  
Forest Coverage ◽  
Log Normal ◽  
Log Normal Distribution

This paper analyses the probability distribution of worldwide forest areas. We find moderate support for a Pareto-type distribution (power law) using FAO data from 1990 to 2015. Power laws are common features of many complex systems in nature. A power law is a plausible model for the world probability distribution of forest areas in all examined years, although the log-normal distribution is a plausible alternative model that cannot be rejected. The random growth of forest areas could generate a power law or log-normal distribution. We study the change in forest coverage using parametric and non-parametric methods. We identified a slight convergence of forest areas over the time reviewed; however, random forest area growth cannot be rejected for most of the distribution of forest areas. Therefore, our results give support to theoretical models of stochastic forest growth.

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